Finite Group Databasebeta

← #36522038

Subgroups — #36522038

Order 22784.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028910C211yesmaximal, characteristic, complemented
2#26023112C211yesmaximal, characteristic, complemented
3#26018829C211yesmaximal, characteristic, complemented
4#26018812C211yesmaximal, characteristic, complemented
5#26018808C211yesmaximal, characteristic, complemented
6#26018799C211yesmaximal, characteristic, complemented
7#26018790C211yesmaximal, characteristic, complemented
8#26018781C211yesmaximal, characteristic, complemented
9#26018777C211yesmaximal, characteristic, complemented
10#26018760C211yesmaximal, characteristic, complemented
11#26018756C211yesmaximal, characteristic, complemented
12#26018747C211yesmaximal, characteristic, complemented
13#26018738C211yesmaximal, characteristic, complemented
14C2×#19151332C211yesmaximal, characteristic, complemented
15C89×#3494C211yesmaximal, characteristic
16#19151659—21no—
17#19151659—21no—
18#19151655C2211yescharacteristic, complemented
19#19151655C2211yescharacteristic, complemented
20#19151651C2211yescharacteristic, complemented
21#19151651C2211yescharacteristic, complemented
22#19151625—21no—
23#19151562C2211yescharacteristic
24C2×C22⋊#10623494C2211yescharacteristic
25#19151554—21no—
26#19151484—21no—
27#19151484—21no—
28#19151473—21no—
29#19151466C2211yescharacteristic, complemented
30#19151464C2211yescharacteristic, complemented
31#19151461C2211yescharacteristic
32C4×C4⋊Dic89C2211yescharacteristic, complemented
33C22⋊C4×Dic89—21no—
34#19151444C2211yescharacteristic, complemented
35C2×#15667919C2211yescharacteristic
36#19151335C2211yescharacteristic, complemented
37#19151335C2211yescharacteristic, complemented
38#19151335C2211yescharacteristic, complemented
39#19151335C2211yescharacteristic, complemented
40#19151332C2211yescharacteristic
41#19151332C2211yescharacteristic
42#19151332C2211yescharacteristic
43#19151332C2211yescharacteristic
44#19151332C2211yescharacteristic
45#19151332C2211yescharacteristic
46#19151332C2211yescharacteristic
47#19151332C2211yescharacteristic
48#19151332C2211yescharacteristic, complemented
49#19151332C2211yescharacteristic, complemented
50#19151332C2211yescharacteristic, complemented
51#19151332C2211yescharacteristic, complemented
52#555×C89—21no—
53#553×C89—21no—
54#553×C89—21no—
55#551×C89—21no—
56#551×C89—21no—
57#547×C89—21no—
58#546×C89—21no—
59#546×C89—21no—
60#544×C89C411yescharacteristic, complemented
61#542×C89C411yescharacteristic, complemented
62#542×C89C411yescharacteristic, complemented
63#540×C89C411yescharacteristic, complemented
64#540×C89C411yescharacteristic, complemented
65#535×C89C411yescharacteristic, complemented
66#532×C89C2211yescharacteristic
67#532×C89C2211yescharacteristic
68#529×C89C2211yescharacteristic
69#529×C89C2211yescharacteristic
70#525×C89C2211yescharacteristic
71C2×#121×C89C2211yescharacteristic
72#520×C89C411yescharacteristic, complemented
73#518×C89C411yescharacteristic, complemented
74C2×#117×C89C2211yescharacteristic
75C23×Dic89—21no—
76C2×#13083558—21no—
77C22×#10623494—21no—
78C2×C4⋊Dic89—21no—
79C2×C4⋊Dic89—21no—
80C2×C22⋊Dic89—21no—
81C2×C4×Dic89—21no—
82C2×C4×Dic89—21no—
83C4⋊#10623494—21no—
84C4⋊#10623494—21no—
85C4⋊#10623494—21no—
86C4⋊#10623494—21no—
87C22⋊#10623494—21no—
88C22⋊#10623494—21no—
89C22⋊#10623494C2311yescharacteristic
90C22⋊#10623494C2311yescharacteristic
91C22⋊#10623494C2311yescharacteristic
92C22⋊#10623494C2311yescharacteristic
93#15667923—21no—
94#15667923—21no—
95C4×#10623494—21no—
96C4×#10623494—21no—
97#15667919—21no—
98#15667919—21no—
99#15667919—21no—
100#15667919—21no—
101#15667919—21no—
102#15667919—21no—
103#15667919C2311yescharacteristic
104#15667919C2311yescharacteristic
105#15667919C2311yescharacteristic
106#15667919C2311yescharacteristic
107C2×#41×C89—21no—
108C2×#41×C89—21no—
109C2×#41×C89C2×C411yescharacteristic
110C22×D4×C89—21no—
111C22×D4×C89C2×C411yescharacteristic
112C23×C4×C89C2311yescharacteristic
113C4⋊Q8×C89—21no—
114C4⋊Q8×C89C2×C411yescharacteristic, complemented
115C4⋊Q8×C89C2×C411yescharacteristic, complemented
116#127×C89C2×C411yescharacteristic, complemented
117#127×C89C2×C411yescharacteristic, complemented
118#126×C89—21no—
119#126×C89—21no—
120#126×C89—21no—
121#126×C89—21no—
122#125×C89—21no—
123#125×C89C2×C411yescharacteristic, complemented
124#125×C89C2×C411yescharacteristic, complemented
125#124×C89—21no—
126#124×C89—21no—
127#124×C89—21no—
128#124×C89—21no—
129#124×C89C2×C411yescharacteristic, complemented
130#124×C89C2×C411yescharacteristic, complemented
131#123×C89—21no—
132#123×C89—21no—
133#123×C89—21no—
134#123×C89—21no—
135#123×C89—21no—
136#123×C89—21no—
137#123×C89—21no—
138#123×C89—21no—
139#123×C89—21no—
140C22⋊Q8×C89—21no—
141C22⋊Q8×C89—21no—
142C22⋊Q8×C89—21no—
143C22⋊Q8×C89—21no—
144C22⋊Q8×C89C2×C411yescharacteristic
145C22⋊Q8×C89C2311yescharacteristic
146#121×C89—21no—
147#121×C89—21no—
148#121×C89—21no—
149#121×C89—21no—
150#121×C89—21no—
151#121×C89—21no—
152#121×C89—21no—
153#121×C89—21no—
154#121×C89—21no—
155#121×C89—21no—
156#121×C89C2×C411yescharacteristic
157#121×C89C2×C411yescharacteristic
158#121×C89C2×C411yescharacteristic
159#121×C89C2311yescharacteristic
160#121×C89C2311yescharacteristic
161#121×C89C2311yescharacteristic
162#120×C89—21no—
163#120×C89—21no—
164#120×C89—21no—
165C4×Q8×C89C2×C411yescharacteristic, complemented
166C4×Q8×C89C2×C411yescharacteristic, complemented
167C4×D4×C89—21no—
168C4×D4×C89—21no—
169C4×D4×C89—21no—
170C4×D4×C89—21no—
171C4×D4×C89—21no—
172C4×D4×C89—21no—
173C4×D4×C89—21no—
174C4×D4×C89—21no—
175C4×D4×C89—21no—
176C4×D4×C89—21no—
177C4×D4×C89C2×C411yescharacteristic, complemented
178C4×D4×C89C2×C411yescharacteristic, complemented
179C4×D4×C89C2×C411yescharacteristic, complemented
180C4×D4×C89C2×C411yescharacteristic, complemented
181C4×D4×C89C2×C411yescharacteristic, complemented
182C4×D4×C89C2×C411yescharacteristic, complemented
183#117×C89—21no—
184#117×C89—21no—
185#117×C89—21no—
186#117×C89C2×C411yescharacteristic
187#117×C89C2×C411yescharacteristic
188#117×C89C2×C411yescharacteristic
189#117×C89C2×C411yescharacteristic
190#117×C89C2×C411yescharacteristic
191#117×C89D411yescharacteristic
192#117×C89D411yescharacteristic
193#117×C89D411yescharacteristic
194#117×C89D411yescharacteristic
195C2×C4⋊C4×C89—21no—
196C2×C4⋊C4×C89C2×C411yescharacteristic
197C2×C4⋊C4×C89D411yescharacteristic
198C2×C4⋊C4×C89D411yescharacteristic
199C2×C22⋊C4×C89—21no—
200C2×C22⋊C4×C89—21no—
201C2×C22⋊C4×C89—21no—
202C2×C22⋊C4×C89D411yescharacteristic
203C2×C22⋊C4×C89D411yescharacteristic
204C2×C42×C89C2311yescharacteristic
205C2×C42×C89C2311yescharacteristic
206C22×Dic89—21no—
207C22×Dic89—21no—
208C22×Dic89—21no—
209C22×Dic89—21no—
210C22×Dic89—42no—
211C22×Dic89—42no—
212C22×Dic89—81no—
213#13083558—42no—
214C2×#10623494—21no—
215C2×#10623494—21no—
216C2×#10623494—21no—
217C2×#10623494—21no—
218C2×#10623494—42no—
219C4⋊Dic89—42no—
220C4⋊Dic89—81no—
221C22⋊Dic89—42no—
222C4×Dic89—42no—
223C4×Dic89—81no—
224C24×C89—21no—
225C24×C89C2×D411yescharacteristic
226#41×C89—42no—
227#41×C89—81no—
228#41×C89—81no—
229#41×C89—81no—
230#41×C89—81no—
231C2×Q8×C89—21no—
232C2×Q8×C89—21no—
233C2×Q8×C89C22×C411yescharacteristic
234C2×D4×C89—21no—
235C2×D4×C89—21no—
236C2×D4×C89—21no—
237C2×D4×C89—21no—
238C2×D4×C89—21no—
239C2×D4×C89—21no—
240C2×D4×C89—21no—
241C2×D4×C89—21no—
242C2×D4×C89—21no—
243C2×D4×C89—21no—
244C2×D4×C89—21no—
245C2×D4×C89—21no—
246C2×D4×C89—42no—
247C2×D4×C89—81no—
248C2×D4×C89—81no—
249C2×D4×C89C22×C411yescharacteristic
250C2×D4×C89C22×C411yescharacteristic
251C2×D4×C89C22×C411yescharacteristic
252C22×C4×C89—21no—
253C22×C4×C89—21no—
254C22×C4×C89—21no—
255C22×C4×C89—21no—
256C22×C4×C89—21no—
257C22×C4×C89—21no—
258C22×C4×C89—21no—
259C22×C4×C89—21no—
260C22×C4×C89—42no—
261C22×C4×C89C22×C411yescharacteristic
262C22×C4×C89C22×C411yescharacteristic
263C22×C4×C89C2×D411yescharacteristic
264C22×C4×C89C2×D411yescharacteristic
265C22×C4×C89C2×D411yescharacteristic
266C22×C4×C89C2×D411yescharacteristic
267C22×C4×C89C2×D411yescharacteristic
268C22×C4×C89C2×D411yescharacteristic
269C22×C4×C89C2×D411yescharacteristic
270C22×C4×C89C2411yescharacteristic
271C4⋊C4×C89—21no—
272C4⋊C4×C89—21no—
273C4⋊C4×C89—21no—
274C4⋊C4×C89—21no—
275C4⋊C4×C89—21no—
276C4⋊C4×C89—21no—
277C4⋊C4×C89—21no—
278C4⋊C4×C89—21no—
279C4⋊C4×C89—21no—
280C4⋊C4×C89—21no—
281C4⋊C4×C89—21no—
282C4⋊C4×C89C22⋊C411yescharacteristic
283C4⋊C4×C89C22⋊C411yescharacteristic
284C4⋊C4×C89C22⋊C411yescharacteristic
285C4⋊C4×C89C22⋊C411yescharacteristic
286C4⋊C4×C89C22⋊C411yescharacteristic
287C4⋊C4×C89C22⋊C411yescharacteristic
288C4⋊C4×C89C22⋊C411yescharacteristic
289C4⋊C4×C89C22⋊C411yescharacteristic
290C4⋊C4×C89C22×C411yescharacteristic
291C4⋊C4×C89C22×C411yescharacteristic
292C4⋊C4×C89C22×C411yescharacteristic
293C4⋊C4×C89C22×C411yescharacteristic
294C22⋊C4×C89—21no—
295C22⋊C4×C89—21no—
296C22⋊C4×C89—21no—
297C22⋊C4×C89—21no—
298C22⋊C4×C89—21no—
299C22⋊C4×C89—21no—
300C22⋊C4×C89—21no—
301C22⋊C4×C89—21no—
302C22⋊C4×C89—21no—
303C22⋊C4×C89—21no—
304C22⋊C4×C89—21no—
305C22⋊C4×C89—21no—
306C22⋊C4×C89—21no—
307C22⋊C4×C89—21no—
308C22⋊C4×C89—21no—
309C22⋊C4×C89—21no—
310C22⋊C4×C89—21no—
311C22⋊C4×C89—21no—
312C22⋊C4×C89—21no—
313C22⋊C4×C89C22⋊C411yescharacteristic
314C22⋊C4×C89C22⋊C411yescharacteristic
315C22⋊C4×C89C22⋊C411yescharacteristic
316C22⋊C4×C89C22⋊C411yescharacteristic
317C22⋊C4×C89C22⋊C411yescharacteristic
318C22⋊C4×C89C22⋊C411yescharacteristic
319C22⋊C4×C89C22⋊C411yescharacteristic
320C22⋊C4×C89C22⋊C411yescharacteristic
321C42×C89—21no—
322C42×C89—21no—
323C42×C89—21no—
324C42×C89C22×C411yescharacteristic
325C42×C89C22×C411yescharacteristic
326C42×C89C22×C411yescharacteristic
327C42×C89C22×C411yescharacteristic
328C42×C89C2×D411yescharacteristic
329C42×C89C2×D411yescharacteristic
330C42×C89C2×D411yescharacteristic
331C42×C89C2×D411yescharacteristic
332C23×C89—21no—
333C23×C89—21no—
334C23×C89—22no—
335C23×C89—21no—
336C23×C89—21no—
337C23×C89—21no—
338C23×C89—41no—
339C23×C89—42no—
340C23×C89—81no—
341C23×C89—81no—
342C23×C89C2×C22⋊C411yescharacteristic
343C23×C89C2×C22⋊C411yescharacteristic
344C23×C89C22×D411yescharacteristic
345Q8×C89—41no—
346Q8×C89—81no—
347Q8×C89—81no—
348D4×C89—41no—
349D4×C89—41no—
350D4×C89—41no—
351D4×C89—42no—
352D4×C89—41no—
353D4×C89—41no—
354D4×C89—41no—
355D4×C89—41no—
356D4×C89—41no—
357D4×C89—41no—
358D4×C89—42no—
359D4×C89—81no—
360D4×C89—81no—
361D4×C89—81no—
362D4×C89—81no—
363D4×C89—81no—
364D4×C89—81no—
365D4×C89—81no—
366C2×C4×C89—21no—
367C2×C4×C89—21no—
368C2×C4×C89—21no—
369C2×C4×C89—21no—
370C2×C4×C89—22no—
371C2×C4×C89—22no—
372C2×C4×C89—21no—
373C2×C4×C89—21no—
374C2×C4×C89—21no—
375C2×C4×C89—21no—
376C2×C4×C89—21no—
377C2×C4×C89—41no—
378C2×C4×C89—41no—
379C2×C4×C89—41no—
380C2×C4×C89—41no—
381C2×C4×C89—41no—
382C2×C4×C89—41no—
383C2×C4×C89—42no—
384C2×C4×C89—81no—
385C2×C4×C89—81no—
386C2×C4×C89—81no—
387C2×C4×C89—81no—
388C2×C4×C89—81no—
389C2×C4×C89—81no—
390C2×C4×C89—81no—
391C2×C4×C89C2×C22⋊C411yescharacteristic
392C2×C4×C89C2×C22⋊C411yescharacteristic
393C2×C4×C89C2×C22⋊C411yescharacteristic
394C2×C4×C89C2×C22⋊C411yescharacteristic
395C2×C4×C89C2×C22⋊C411yescharacteristic
396C2×C4×C89C2×C22⋊C411yescharacteristic
397C2×C4×C89C2×C22⋊C411yescharacteristic
398C2×C4×C89C2×C22⋊C411yescharacteristic
399C2×C4×C89C2×C22⋊C411yescharacteristic
400C2×C4×C89C2×C22⋊C411yescharacteristic
401C2×C4×C89C23×C411yescharacteristic
402C2×C4×C89C22×D411yescharacteristic
403C2×Dic89—22no—
404C2×Dic89—41no—
405C2×Dic89—41no—
406C2×Dic89—41no—
407C2×Dic89—41no—
408C2×Dic89—41no—
409C2×Dic89—41no—
410C2×Dic89—41no—
411C2×Dic89—41no—
412C2×Dic89—41no—
413C2×Dic89—41no—
414C2×Dic89—41no—
415C2×Dic89—84no—
416#10623494—41no—
417#10623494—41no—
418#10623494—41no—
419#10623494—41no—
420C22×C89—21no—
421C22×C89—21no—
422C22×C89—21no—
423C22×C89—21no—
424C22×C89—21no—
425C22×C89—21no—
426C22×C89—21no—
427C22×C89—42no—
428C22×C89—42no—
429C22×C89—41no—
430C22×C89—41no—
431C22×C89—41no—
432C22×C89—41no—
433C22×C89—41no—
434C22×C89—41no—
435C22×C89—41no—
436C22×C89—41no—
437C22×C89—41no—
438C22×C89—162no—
439C22×C89#41012yes—
440C22×C89C22×C22⋊C411yescharacteristic
441C22×C89#57611yescharacteristic
442C22×C89#57711yescharacteristic
443C4×C89—21no—
444C4×C89—21no—
445C4×C89—21no—
446C4×C89—21no—
447C4×C89—21no—
448C4×C89—21no—
449C4×C89—21no—
450C4×C89—21no—
451C4×C89—21no—
452C4×C89—21no—
453C4×C89—21no—
454C4×C89—21no—
455C4×C89—41no—
456C4×C89—41no—
457C4×C89—41no—
458C4×C89—41no—
459C4×C89—41no—
460Dic89—42no—
461Dic89—81no—
462Dic89—81no—
463Dic89—81no—
464#17604—891nomaximal, Sylow
465C2×C89—21no—
466C2×C89—21no—
467C2×C89—22no—
468C2×C89—41no—
469C2×C89—81no—
470C2×C89—81no—
471C2×C89—81no—
472C2×C89C2×#41011yescharacteristic
473C2×C89#289711yescharacteristic
474C2×C89#290111yescharacteristic
475#3494D8911yescharacteristic
476#2924—891no—
477#2343—891no—
478#1521—891no—
479#1517—891no—
480#1516—891no—
481#1514—891no—
482#1512—891no—
483#1510—891no—
484#1509—891no—
485#1505—891no—
486#1504—891no—
487#1502—891no—
488#1500—891no—
489C2×#327—891no—
490C89#1760411yescharacteristic, complemented, Sylow
491#555—21no—
492#553—21no—
493#553—21no—
494#551—21no—
495#551—21no—
496#547—21no—
497#546—21no—
498#546—21no—
499#544Dic8911yescharacteristic, complemented
500#542Dic8911yescharacteristic, complemented
501#542Dic8911yescharacteristic, complemented
502#540Dic8911yescharacteristic, complemented
503#540Dic8911yescharacteristic, complemented
504#535Dic8911yescharacteristic, complemented
505#532C2×D8911yescharacteristic
506#532C2×D8911yescharacteristic
507#529C2×D8911yescharacteristic
508#529C2×D8911yescharacteristic
509#525C2×D8911yescharacteristic
510C2×#121C2×D8911yescharacteristic
511#520Dic8911yescharacteristic, complemented
512#518Dic8911yescharacteristic, complemented
513C2×#117C2×D8911yescharacteristic
514#433—1781no—
515#433—1781no—
516#432—891no—
517#432—891no—
518#431—891no—
519#431—891no—
520#424—1781no—
521#407—891no—
522C2×C22⋊C8—891no—
523#405—1781no—
524#387—1781no—
525#387—1781no—
526#385—1781no—
527#383—891no—
528#382—891no—
529#381—891no—
530C4×C4⋊C4—891no—
531C4×C22⋊C4—1781no—
532#376—891no—
533C2×#95—891no—
534#328—891no—
535#328—891no—
536#328—891no—
537#328—891no—
538#327—891no—
539#327—891no—
540#327—891no—
541#327—891no—
542#327—891no—
543#327—891no—
544#327—891no—
545#327—891no—
546#327—891no—
547#327—891no—
548#327—891no—
549#327—891no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41C2×Dic8911yescharacteristic
553C22×D4—21no—
554C22×D4C2×Dic8911yescharacteristic
555C23×C4—1781no—
556C23×C4C22×D8911yescharacteristic
557C2×M16—1781no—
558C22×C8—1781no—
559C4⋊Q8—21no—
560C4⋊Q8C2×Dic8911yescharacteristic, complemented
561C4⋊Q8C2×Dic8911yescharacteristic, complemented
562#127C2×Dic8911yescharacteristic, complemented
563#127C2×Dic8911yescharacteristic, complemented
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125C2×Dic8911yescharacteristic, complemented
570#125C2×Dic8911yescharacteristic, complemented
571#124—21no—
572#124—21no—
573#124—21no—
574#124—21no—
575#124C2×Dic8911yescharacteristic, complemented
576#124C2×Dic8911yescharacteristic, complemented
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8C2×Dic8911yescharacteristic
591C22⋊Q8C22×D8911yescharacteristic
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121C2×Dic8911yescharacteristic
603#121C2×Dic8911yescharacteristic
604#121C2×Dic8911yescharacteristic
605#121C22×D8911yescharacteristic
606#121C22×D8911yescharacteristic
607#121C22×D8911yescharacteristic
608#120—21no—
609#120—21no—
610#120—21no—
611C4×Q8C2×Dic8911yescharacteristic, complemented
612C4×Q8C2×Dic8911yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—21no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4C2×Dic8911yescharacteristic, complemented
624C4×D4C2×Dic8911yescharacteristic, complemented
625C4×D4C2×Dic8911yescharacteristic, complemented
626C4×D4C2×Dic8911yescharacteristic, complemented
627C4×D4C2×Dic8911yescharacteristic, complemented
628C4×D4C2×Dic8911yescharacteristic, complemented
629#117—21no—
630#117—21no—
631#117—21no—
632#117C2×Dic8911yescharacteristic
633#117C2×Dic8911yescharacteristic
634#117C2×Dic8911yescharacteristic
635#117C2×Dic8911yescharacteristic
636#117C2×Dic8911yescharacteristic
637#117C22⋊D8911yescharacteristic
638#117C22⋊D8911yescharacteristic
639#117C22⋊D8911yescharacteristic
640#117C22⋊D8911yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—1781no—
643C2×C4⋊C4—1781no—
644C2×C4⋊C4C2×Dic8911yescharacteristic
645C2×C4⋊C4C22⋊D8911yescharacteristic
646C2×C4⋊C4C22⋊D8911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—1781no—
651C2×C22⋊C4C22⋊D8911yescharacteristic
652C2×C22⋊C4C22⋊D8911yescharacteristic
653C2×C42—1781no—
654C2×C42—1781no—
655C2×C42C22×D8911yescharacteristic
656C2×C42C22×D8911yescharacteristic
657C4⋊C8—1781no—
658C4⋊C8—1781no—
659C4⋊C8—1781no—
660C4⋊C8—1781no—
661C22⋊C8—891no—
662C22⋊C8—891no—
663C22⋊C8—891no—
664C22⋊C8—891no—
665C22⋊C8—1781no—
666C22⋊C8—1781no—
667#97—1781no—
668#97—1781no—
669C4×C8—1781no—
670C4×C8—1781no—
671#95—891no—
672#95—891no—
673#95—891no—
674#95—891no—
675#95—1781no—
676#95—1781no—
677#95—1781no—
678#95—1781no—
679#95—1781no—
680#95—1781no—
681C24—21no—
682C24C2×C22⋊D8911yescharacteristic
683#41—42no—
684#41—81no—
685#41—81no—
686#41—81no—
687#41—81no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8C22×Dic8911yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4C22×Dic8911yescharacteristic
707C2×D4C22×Dic8911yescharacteristic
708C2×D4C22×Dic8911yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—42no—
718C22×C4—3562no—
719C22×C4—3562no—
720C22×C4—1781no—
721C22×C4—1781no—
722C22×C4—1781no—
723C22×C4—1781no—
724C22×C4—7121no—
725C22×C4C22×Dic8911yescharacteristic
726C22×C4C22×Dic8911yescharacteristic
727C22×C4C2×C22⋊D8911yescharacteristic
728C22×C4C2×C22⋊D8911yescharacteristic
729C22×C4C2×C22⋊D8911yescharacteristic
730C22×C4C2×C22⋊D8911yescharacteristic
731C22×C4C2×C22⋊D8911yescharacteristic
732C22×C4C2×C22⋊D8911yescharacteristic
733C22×C4C2×C22⋊D8911yescharacteristic
734C22×C4C23×D8911yescharacteristic
735M16—3562no—
736C2×C8—3562no—
737C2×C8—1781no—
738C2×C8—1781no—
739C2×C8—1781no—
740C2×C8—1781no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—3562no—
753C4⋊C4—7121no—
754C4⋊C4C22⋊Dic8911yescharacteristic
755C4⋊C4C22⋊Dic8911yescharacteristic
756C4⋊C4C22⋊Dic8911yescharacteristic
757C4⋊C4C22⋊Dic8911yescharacteristic
758C4⋊C4C22⋊Dic8911yescharacteristic
759C4⋊C4C22⋊Dic8911yescharacteristic
760C4⋊C4C22⋊Dic8911yescharacteristic
761C4⋊C4C22⋊Dic8911yescharacteristic
762C4⋊C4C22×Dic8911yescharacteristic
763C4⋊C4C22×Dic8911yescharacteristic
764C4⋊C4C22×Dic8911yescharacteristic
765C4⋊C4C22×Dic8911yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—3562no—
786C22⋊C4C22⋊Dic8911yescharacteristic
787C22⋊C4C22⋊Dic8911yescharacteristic
788C22⋊C4C22⋊Dic8911yescharacteristic
789C22⋊C4C22⋊Dic8911yescharacteristic
790C22⋊C4C22⋊Dic8911yescharacteristic
791C22⋊C4C22⋊Dic8911yescharacteristic
792C22⋊C4C22⋊Dic8911yescharacteristic
793C22⋊C4C22⋊Dic8911yescharacteristic
794C42—21no—
795C42—21no—
796C42—21no—
797C42—3562no—
798C42—7121no—
799C42C22×Dic8911yescharacteristic
800C42C22×Dic8911yescharacteristic
801C42C22×Dic8911yescharacteristic
802C42C22×Dic8911yescharacteristic
803C42C2×C22⋊D8911yescharacteristic
804C42C2×C22⋊D8911yescharacteristic
805C42C2×C22⋊D8911yescharacteristic
806C42C2×C22⋊D8911yescharacteristic
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23C2×C22⋊Dic8911yescharacteristic
818C23C2×C22⋊Dic8911yescharacteristic
819C23C22×C22⋊D8911yescharacteristic
820Q8—41no—
821Q8—81no—
822Q8—81no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—81no—
835D4—81no—
836D4—81no—
837D4—81no—
838D4—81no—
839D4—81no—
840D4—81no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—3561no—
867C2×C4—3561no—
868C2×C4—3561no—
869C2×C4—3561no—
870C2×C4—3561no—
871C2×C4—3561no—
872C2×C4—3561no—
873C2×C4—3561no—
874C2×C4—3561no—
875C2×C4—3561no—
876C2×C4—3561no—
877C2×C4—1782no—
878C2×C4—7124no—
879C2×C4C2×C22⋊Dic8911yescharacteristic
880C2×C4C2×C22⋊Dic8911yescharacteristic
881C2×C4C2×C22⋊Dic8911yescharacteristic
882C2×C4C2×C22⋊Dic8911yescharacteristic
883C2×C4C2×C22⋊Dic8911yescharacteristic
884C2×C4C2×C22⋊Dic8911yescharacteristic
885C2×C4C2×C22⋊Dic8911yescharacteristic
886C2×C4C2×C22⋊Dic8911yescharacteristic
887C2×C4C2×C22⋊Dic8911yescharacteristic
888C2×C4C2×C22⋊Dic8911yescharacteristic
889C2×C4C23×Dic8911yescharacteristic
890C2×C4C22×C22⋊D8911yescharacteristic
891C8—3561no—
892C8—3561no—
893C8—3561no—
894C8—3561no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—162no—
914C22#1915157212yes—
915C22C22×C22⋊Dic8911yescharacteristic
916C22#1915240111yescharacteristic
917C22#1915240911yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—3562no—
936C4—7121no—
937C4—7121no—
938C4—7121no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—81no—
946C2C2×#1915157211yescharacteristic
947C2#2602877811yescharacteristic
948C2#2602879911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
Fitting, prime radicalC89×#3494C2
socleC22×C89C22×C22⋊C4
cosocleC22×C4×C89C24
hypercenter#3494D89
hypocenterC89#17604
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26028910C2semidirect
2. #26023112C2semidirect
3. #26018829C2semidirect
4. #26018812C2semidirect
5. #26018808C2semidirect
6. #26018799C2semidirect
7. #26018790C2semidirect
8. #26018781C2semidirect
9. #26018777C2semidirect
10. #26018760C2semidirect
11. #26018756C2semidirect
12. #26018747C2semidirect
13. #26018738C2semidirect
14. C2×#19151332C2semidirect
18. #19151655C22semidirect
19. #19151655C22semidirect
20. #19151651C22semidirect
21. #19151651C22semidirect
29. #19151466C22semidirect
30. #19151464C22semidirect
32. C4×C4⋊Dic89C22semidirect
34. #19151444C22semidirect
36. #19151335C22semidirect
37. #19151335C22semidirect
38. #19151335C22semidirect
39. #19151335C22semidirect
48. #19151332C22semidirect
49. #19151332C22semidirect
50. #19151332C22semidirect
51. #19151332C22semidirect
60. #544×C89C4semidirect
61. #542×C89C4semidirect
62. #542×C89C4semidirect
63. #540×C89C4semidirect
64. #540×C89C4semidirect
65. #535×C89C4semidirect
72. #520×C89C4semidirect
73. #518×C89C4semidirect
114. C4⋊Q8×C89C2×C4semidirect
115. C4⋊Q8×C89C2×C4semidirect
116. #127×C89C2×C4semidirect
117. #127×C89C2×C4semidirect
123. #125×C89C2×C4semidirect
124. #125×C89C2×C4semidirect
129. #124×C89C2×C4semidirect
130. #124×C89C2×C4semidirect
165. C4×Q8×C89C2×C4semidirect
166. C4×Q8×C89C2×C4semidirect
177. C4×D4×C89C2×C4semidirect
178. C4×D4×C89C2×C4semidirect
179. C4×D4×C89C2×C4semidirect
180. C4×D4×C89C2×C4semidirect
181. C4×D4×C89C2×C4semidirect
182. C4×D4×C89C2×C4semidirect
490. C89#17604semidirect
499. #544Dic89semidirect
500. #542Dic89semidirect
501. #542Dic89semidirect
502. #540Dic89semidirect
503. #540Dic89semidirect
504. #535Dic89semidirect
511. #520Dic89semidirect
512. #518Dic89semidirect
560. C4⋊Q8C2×Dic89semidirect
561. C4⋊Q8C2×Dic89semidirect
562. #127C2×Dic89semidirect
563. #127C2×Dic89semidirect
569. #125C2×Dic89semidirect
570. #125C2×Dic89semidirect
575. #124C2×Dic89semidirect
576. #124C2×Dic89semidirect
611. C4×Q8C2×Dic89semidirect
612. C4×Q8C2×Dic89semidirect
623. C4×D4C2×Dic89semidirect
624. C4×D4C2×Dic89semidirect
625. C4×D4C2×Dic89semidirect
626. C4×D4C2×Dic89semidirect
627. C4×D4C2×Dic89semidirect
628. C4×D4C2×Dic89semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260289102
#260231122
#260188292
#260188122
#260188082
#260187992
#260187902
#260187812
#260187772
#260187602
#260187562
#260187472
#260187382
C2×#191513322
C89×#34942
#1760489